1988 5KSQ in Manhattan Won't Start

["Christopher J. Ritchie" <cjr1@gte.net>]

Any recommendations for troubleshooting a "no start" condition for this
car?  Any anomalies peculiar to this car for which I should check before
the usual troubleshooting procedures?  The battery is good, and the starter
cranks the engine over.  However, the engine won't catch - not even a cough
or sputter.  The car has been sitting for 3 days in a very humid and wet
atmosphere.  I tried cranking for about 3 hours (off and on).  The battery
is getting weaker.  I won't try it again for awhile.  As you can tell from
my description, I suspect electrical - no spark.  Is this car known for
this condition?  The forecast here is for rain and humidity for the next
few days.

I am at a disadvantage here.  Away from home, no tools, no battery charger,
no helper.  The car is on the street, and alternate side parking rules are
in effect.  But I won't need to move the car now until Tuesday, May 12 at 8
AM.  The NYPD is very insistent on this point.  

I might be able to scrounge up some basic tools and an inexperienced
assistant.  But I won't have much of an opportunity to play around with a
low battery, little or no tools, and no experience with this car (I am a
new owner.).

Where is a good place to start?  I will probably do the inside of the
distributor and its cap and the spark plug wires with WD-40.

Any recommendations on service near Manhattan's Upper East Side?  The
Yellow Pages list an Audi dealer, Zumbach Motors, on West 54th.  The Yellow
Pages also list a repair shop, Golf Auto Repair, one block from the car. 
They advertise that they specialize in Audis.  

Any advice would greatly be appreciated.